Monografie Matematyczne

Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals

Authors: Kislyakov, Sergey, Kruglyak, Natan

  • Quick and concise introduction to several important classical topics of real analysis Exposition of powerful results of recent research in a self-contained manner, making them accessible to beginners Presents results not yet available in existing literature Contains descriptions of new techniques which may be useful in other research problems  ​

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About this book

In this book we suggest a unified method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and ill-posed problems and most widely used in interpolation theory. The constructions are based on far-reaching refinements of the classical Calderón–Zygmund decomposition. These new Calderón–Zygmund decompositions in turn are produced with the help of new covering theorems that combine many remarkable features of classical results established by Besicovitch, Whitney and Wiener. In many cases the minimizers constructed in the book are stable (i.e., remain near-minimizers) under the action of Calderón–Zygmund singular integral operators.

The book is divided into two parts. While the new method is presented in great detail in the second part, the first is mainly devoted to the prerequisites needed for a self-contained presentation of the main topic. There we discuss the classical covering results mentioned above, various spectacular applications of the classical Calderón–Zygmund decompositions, and the relationship of all this to real interpolation. It also serves as a quick introduction to such important topics as spaces of smooth functions or singular integrals.

Reviews

From the reviews:

“The monograph is a good source of information on spaces of smooth functions and real interpolation methods. … the monograph could be a good reference on methods and results in the area. The book is highly recommended for specialists in approximation theory, harmonic analysis, functional analysis, and related areas. … the monograph should be interesting for specialists in applied mathematics and computer science. Graduate students specializing in analysis should find many interesting topics here, as well as motivation for further research.” (Alexander V. Tovstolis, Mathematical Reviews, August, 2013)

“This book consists of two parts. … Each chapter closes with comments, historical remarks and further references. Everybody who is interested in this topic should consult this important book. Without doubt, this monograph will stimulate further research.” (Manfred Tasche, zbMATH, Vol. 1270, 2013)

Table of contents (11 chapters)

  • Classical Calderón–Zygmund decomposition and real interpolation

    Kislyakov, Sergey (et al.)

    Pages 23-45

  • Singular integrals

    Kislyakov, Sergey (et al.)

    Pages 47-64

  • Classical covering theorems

    Kislyakov, Sergey (et al.)

    Pages 65-89

  • Spaces of smooth functions and operators on them

    Kislyakov, Sergey (et al.)

    Pages 91-122

  • Some topics in interpolation

    Kislyakov, Sergey (et al.)

    Pages 123-144

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-0469-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-0348-0468-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-0348-0752-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular Integrals
Authors
Series Title
Monografie Matematyczne
Series Volume
74
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0469-1
DOI
10.1007/978-3-0348-0469-1
Hardcover ISBN
978-3-0348-0468-4
Softcover ISBN
978-3-0348-0752-4
Series ISSN
0077-0507
Edition Number
1
Number of Pages
X, 322
Topics